*2.4. Physical Parameters*

Following an engineering approach, the quantities *CF* (local skin friction coefficient) and *Nus* (Nusselt number) are expressed as follows:

$$C\_F = \frac{2\tau\_{rs}}{\rho\_f u\_w^2} \tag{16}$$

where

$$\tau\_{rs} = \mu\_{\rm nf} \left( \frac{\partial u}{\partial r} - \frac{u}{r + R} \right) - b \left[ - \left( \frac{\partial u}{\partial r} - \frac{u}{r + R} \right) \right]^n \Big|\_{r = 0} \tag{17}$$

After transformation, the reduced skin friction coefficient becomes

$$\frac{1}{2}\text{Re}\_{b}\overset{1}{\mathbb{P}^{\pi+1}}\mathbb{C}\_{F} = \Sigma\_{1}B\_{1}\left(F''(0) - \frac{F'(0)}{B}\right) - \left(-\left(F''(0) - \frac{F'(0)}{B}\right)\right)^{n}.\tag{18}$$

The heat transfer rate at the surface, *Nus* (Nusselt number), is

*Nus* = *sqw k f*(*Tw* − *<sup>T</sup>*∞), (19)

where

$$q\_w = -k\_{nf} \left( \frac{\partial T}{\partial r} \right) \Big|\_{r=0}. \tag{20}$$

After transformation, the reduced Nusselt number becomes

$$\operatorname{Re}\_{\theta}^{\frac{-1}{n+1}} \operatorname{Nu}\_{\theta} = -\Sigma\_{4} \theta'(0). \tag{21}$$
